空间等离子体和单粒子的运动、KineticTheory和MHD简介课件.ppt

1、1空间等离子体和单粒子的运动、Kinetic Theory 和 MHD 简介Outline:n等离子体的定义nDebye长度和等离子体的特性n空间等离子体n单个带电粒子的运动n回旋波nGuiding center motionn磁矩守恒量n磁镜效应nTrapped particlesn辐射带n电离层n极光的产生n磁冻结效应nKinetic theory简介nMHD简介23等离子体n等离子体的定义:由由自由电子和自由离子组成的集合体（气体），自由电子和自由离子组成的集合体（气体），其正负电荷数目相同。在平均作用的意义上，等离子体对其正负电荷数目相同。在平均作用的意义上，等离子体对外呈现电中性。外

2、呈现电中性。等离子体的直接特性：等离子体的直接特性：自由离子和自由电子占主导地位自由离子和自由电子占主导地位（即带电粒子所受到的势能远小于粒子热（即带电粒子所受到的势能远小于粒子热运动的动能），随机的热运动克服库仑势。运动的动能），随机的热运动克服库仑势。4PropertyGasPlasmaElectrical ConductivityVery lowAir is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimete

3、r.Usually very highFor many purposes,the conductivity of a plasma may be treated as infinite.Independently acting speciesOne All gas particles behave in a similar way,influenced by gravity and by collisions with one another.Two or threeElectrons,ions,protons and neutrons can be distinguished by the

4、sign and value of their charge so that they behave independently in many circumstances,with different bulk velocities and temperatures,allowing phenomena such as new types of waves and instabilities.Velocity distributionMaxwellianCollisions usually lead to a Maxwellian velocity distribution of all g

5、as particles,with very few relatively fast particles.Often non-MaxwellianCollisional interactions are often weak in hot plasmas and external forcing can drive the plasma far from local equilibrium and lead to a significant population of unusually fast particles.InteractionsBinaryTwo-particle collisi

6、ons are the rule,three-body collisions extremely rare.CollectiveWaves,or organized motion of plasma,are very important because the particles can interact at long ranges through the electric and magnetic forces.http:/en.wikipedia.org/wiki/Plasma_%28physics%295See http:/en.wikipedia.org/wiki/Plasma_%2

7、8physics%29Plasma lamp 分离的正离子和电子是否会在电场力的库仑相互作用下结合成电中性原子或者分子？频繁的带电粒子碰撞对等离子体的影响是什么？6什么样的条件使得等离子体稳定存在？1.保持电中性2.自由粒子的存在3.发生碰撞的几率低7德拜屏蔽(Debye Shielding)等离子体存在一个特征长度，在此特征长度以外，带电粒子间库仑势场因为屏蔽效应迅速减弱。这个特征长度定义为Debye length。200enkTeD8Debye Length由温度和带电粒子的密度共同决定9Debye and Coulomb potentialrQ041)exp(410DrrQ库仑势德拜势1

8、0德拜屏蔽(Debye Shielding)统计物理指出自由粒子在相空间*的分布大致如下：eeeekTqVmkTmn221230eexp2(v)f*相空间指（vx,vy,vz,rx,ry,rz）组成的坐标空间11解Poisson方程 eqkTeenexp10002)exp(410DrrQ2002enkTeD1209.6nTeD德拜长度的快速估算Debye Length in cmTe in kn0 in cm-313研究对象尺寸要求DL保持等离子体电中性14典型的德拜长度PlasmaDensitne(m-3)Electron temperatureT(K)MagneticFieldB(T)De

9、byeLengthD(m)Solar core1032107-1011Tokamak102010810104Gas discharge1016104-104Ionosphere1012103105103Magnetosphere107107108102Solar wind10610510910Interstellar medium105104101010Intergalactic medium1106-105http:/en.wikipedia.org/wiki/Debye_length#Debye_length_in_silicon15Debye length vs spacecraftnS

10、pacecraft potential光电子效应产生的电荷16Debye sphere13DeDnN德拜球的定义如下：ND讨论了自由带电粒子的中的“自由问题”172123nTND13DeDnN20enkTeeD18如何联系自由带电粒子和ND？1ekTe库仑势能远小于粒子热运动的动能考虑极限条件下：311minenr于是：min041re32311414120DeeeNnkTekTe1ekTe13DeDnN19Plasma frequencyx00 xenE+-Possible electron plasma oscillationx20 xenEedtxdme02022)(单个电子的运动方程整

11、理后：002022xmendtxdeHarmonic oscillator equation212102eepemen谐振子方程的特征频率2等离子体对碰撞的限制22sDspsCRelationship between Plasma Frequency,Debye length,and thermal speed23散射问题（碰撞）n和电中性粒子的碰撞n和带电粒子的碰撞24碰撞频率Cnvf41 vC31 vf Hot Plasma is collisionless25研究对象是否是等离子体的判据总结nDebye shieldingnFree charged particlenLess colli

12、sion with neutral26等离子体中的量子效应？2332332/kmnTeeeHeisenbergs uncertainty principleLHS:The boundary of classical and quantum regime27空间中的等离子体n太阳风n磁层n辐射带n电离层空间等离子体的典型参数n太阳风：ne=5 cm-3,Te=105k,B=5nTn磁层-辐射带：ne=1 cm-3,Te=107k,B=100-1000nTn磁层磁尾：ne=10-2 cm-3,Te=105k,B=30nTn电离层：ne=105 cm-3,Te=103k,B=104nT2829Qui

13、z 31.1.何为何为“等离子体等离子体”？2.2.为什么太阳风等离子体能够保持电离状态而不为什么太阳风等离子体能够保持电离状态而不会发生离子和电子的复合？会发生离子和电子的复合？3.3.1AU1AU处太阳风质子热速度为处太阳风质子热速度为35km/s35km/s，试推算太阳，试推算太阳风质子温度。风质子温度。30研究等离子体的方法n单粒子运动n流体力学的方法（Magnetohydrodynamics）nKinetic theory31单个带电粒子的运动n库仑力和洛仑兹力BVEFqq32回旋运动yxqBvvmdtdmqvBVF0zvmn受洛仑兹力影响的带电离子的运动方程xyqBvvmxxvmq

14、Bv yyvmqBv 假设在均匀磁场中zBeB33Cyclotron Frequencyn有磁场存在的等离子体mqBg34带电粒子回旋运动的轨迹mBqgCyclotron Frequency(gyrofrequency)22yxvvvBqmvvrggNote:gyroradius35Guiding center and pitch angle(俯仰角)/1tanvv36Drift motion Electric Drift 37其它几种漂移运动nPolarization DriftnMagnetic Gradient DriftnGeneral Force DriftnCurvature Dr

15、ift38Guiding Center motion39磁矩守恒nMagnetic momentBWBmv2240磁镜效应41磁镜效应推导121222sinsinBBBmvBmv2sin2222maxB90maxsinBB42Loss conemaxminminsinBB43Van Allen辐射带Trapped charged particles44The outer beltnThe outer belt consists mainly of high energy(0.110 MeV)electrons nThe large outer radiation belt extends fr

16、om an altitude of about three to ten Earth radii(RE)or 13,000 to 19,000 kilometres above the Earths surface.Its greatest intensity is usually around 45 RE.45Inner beltnThe inner Van Allen Belt extends from an altitude of 10010,000 km(0.01 to 1.5 Earth radii)nIons energy exceeding 100 MeV and electro

17、ns in the range of hundreds of keV,trapped by the strong(relative to the outer belts)magnetic fields in the region nIt is believed that protons of energies exceeding 50 MeV in the lower belts at lower altitudes are the result of the beta decay of neutrons created by cosmic ray collisions with nuclei

18、 of the upper atmosphere.The source of lower energy protons is believed to be proton diffusion due to changes in the magnetic field during geomagnetic storms 46地面实验室模拟的辐射带47木星的辐射带48Aurorahttp:/en.wikipedia.org/wiki/Aurora_(astronomy)49Kinetic theorynDistribution function kTmkTmnf2exp22023vvv ndvdvdv

19、fzyxv50Kinetic theory0),(tfdtdrvvxdtdtdtdvvNote:51等离子体中的Vlasov方程0fmqftfvxBvEv52类似Maxwellian分布曲线53卫星位于地球bow shock以外卫星位于磁尾54离子束流的速度、压强和温度 vdfnb31vvv vdfmbb3)(vvvvvP/000000PPPPnkTP TThe 1st order momentThe 2nd order moment55典型Flux的范围Non-Maxwellian distribution functionnKappa distribution-power law dist

20、ribution5657MHD简介n流体力学的理论在于寻求宏观参量的演化方程；（宏观参量指：n(r,t),v(r,t),p(r,t),T(r,t)etc.）；n当单粒子理论中的粒子所带电荷、质量无限变化时（如：e=e/M,m=m/M），等离子体的德拜长度、回旋半径和回旋频率等保持不变（可作为流体处理）。580smsmsntnV连续性方程59磁冻结（frozen-in condition）BvBt0BvE0jBvBtt BEFaradays law60magnetopause61n磁压022BpBn等离子体beta常数202Bp62n磁声速（Alfven velocity）iAnmBv022No

21、te:sound speednmppcs263MHD使用范围ggrL 64Quasi-PerpendicularQuasi-ParallelDiffuse ionsFABIon Foreshock BoundaryBEarthField-aligned beamsSpecularly reflected ionsIntermediate distributionDiffuse distribution 地球舷激波周围离子加速的情况65Dynamic of the Earths Bow Shock The dynamic of the Earths bowshock creates variations of the localBn,which can lead to particle release in turn.66磁矩守恒失效的情况总结：n简单介绍了等离子体的概念；n单粒子运动nKinetic theorynMHD6768Thank you!